## Microwave Land Emissivity Modelling

### Overview

- Mean AMSU emissivity curves sorted out by scan position and by surface type have shown remarkably stable patterns over the months (Karbou et al. 2005). This property is very interesting because it means that it is possible to characterize each surface type by a function that describes the emissivity angular and the frequency variations. It also means that, at a first stage, a one month period of emissivity estimations is enough to derive such functions
- Two microwave emissivity parameterizations have been proposed to estimate the land emissivity at AMSU frequencies and the scanning conditions in order to help processing AMSU measurements over land surfaces (Karbou 2005). Both parameterizations are derived from previously calculated land emissivities directly from satellite observations and take into account different surface types from bare soil to areas with high vegetation density. The first parameterization uses best-fit functions derived from microwave observations whereas the second parameterization is based on the first one with the use of a mean nadir emissivity map at 23.8 GHz. The use of a nadir emissivity map has been found useful for a more reliable surface description.
- the emissivity model has been developed using data from a limited area (+/- 60° in latitude and longitude). The model’s coefficients have been updated using global data.
- The emissivity parameterizations have been successfully evaluated by comparing emissivity and Tb simulations to target emissivity and to Tb observations.

### The best-fit functions

The parameterization coefficients are function of the frequency, of the scan position and also of the surface types (according to the BATS climatology). The coefficients as well as near-nadir mean AMSU-A and AMSU-B emissivity maps are computed over a one month period. Given a frequency and a surface type, the AMSU-A emissivity could be expressed by :

FOV is the AMSU-A scan position (varies from 1 to 30). P1, P2, P3, P4, P5 and P6 are the polynomial fit coefficients for a given AMSU-A frequency (23, 31, 50 and 89 GHz).

In the same manner, the AMSU-B emissivity could modelled using :

FOV is the AMSU-B scan position (varies from 1 to 90). P1, P2, P3, P4, P5 and P6 are the polynomial fit coefficients for a given AMSU-B frequency (89 GHz and 150 GHz).

By construction, the coefficient P6 represents the mean emissivity at nadir and could be updated using near nadir emissivity atlases. It is worthy to mention that the best-fit functions could be constructed so that the P6 coefficients represents the emissivity at 53°. In this case, mean emissivity atlases from SSM/I could be used to describe the emissivity variation with the zenith angle.

### Evaluation of the parameterization coefficients

- The parametrizations have been tested and successfully evaluated using data from year 2000 (Karbou 2005). In the last mentionned study, the parametrization coefficients have been calculated over a limited region : (60S to 60N) in latitudes and (60W to 60E) in longitudes. The parametrization coefficients have been updated to include multi-sensor data at a global scale.
- The last 2 weeks of August 2005 have been used to derive global best-fit coefficients for AMSU-A and AMSU-B. The following figure shows Mean emissivities for AMSU-A surface channels sorted out by FOV position and by surface type. Asterisks symbols indicate mean emissivities derived from satellite observations and solid curves are for polynomial functions to fit the angular variation of the emissivity. Results are given for (a) AMSU-A channel 1 (23.8 GHz), (b) channel 2 (31 GHz), (c) channel 3 (50 GHz) and (d) channel 15 (89 GHz)

- The first two weeks of September 2005 have been used to evaluate the AMSU angular parameterizations. "True emissivities" are emissivities directly calculated from observations and "simulated emissivities" are emissivities calculated using our parameterizations.
- Two methods have been used to simulate the emissivities : (1) the first one uses only the angular parameterization coefficients (called hereafter SIM1) and (2) the second method uses both the parameterization coefficients and a near-nadir mean AMSU emissivity atlas averaged using data from August 2005 (called hereafter SIM2). In this case, mean emissivities at nadir will replace the coefficient P6.
- Global statistics are given in the following tables.

AMSU-A channels | Mean bias (TRUE-SIM1) | Std (TRUE-SIM1) | Correlation (TRUE, SIM1) |

1 | -0.0001 | 0.0534 | 0.7786 |

2 | -0.0000 | 0.0514 | 0.7978 |

3 | -0.0003 | 0.0470 | 0.7917 |

15 | -0.0012 | 0.0533 | 0.7670 |

AMSU-A channels | Mean bias (TRUE-SIM2) | Std (TRUE-SIM2) | Correlation (TRUE, SIM2) |

1 | -0.0054 | 0.0266 | 0.9519 |

2 | -0.0054 | 0.0253 | 0.9571 |

3 | -0.0028 | 0.0248 | 0.9488 |

15 | -0.0025 | 0.0312 | 0.9276 |